STA325 STATISTICAL INFERENCE

3 Hours/Week, 3 Credits

Point estimation: basic concepts, principles of point estimation. Method of point estimation: method of maximum likelihood, method of moments, method of least squares, method of minimum chi-squares, method of minimum variance, and Bayes’ method. Properties of point estimators: unbiasedness, sufficiency, consistency, efficiency, asymptotic efficiency. Cramer-Rao lower bound, MVB estimate Interval estimation: concept of central and non-central confidence interval. Confidence interval for parameters of normal, binomial and Poisson distributions, large sample confidence interval. Parametric tests: basic concepts, simple hypothesis & composite hypothesis, critical region, best critical region, Neyman-Pearson fundamental lemma, most powerful tests, uniformly most powerful critical region, ump tests. Non-parametric tests: tests based on runs, tests of goodness of fit. Rank order statistics. Other one sample and paired sample techniques. The sign test and signed rank test. The general two sample problem. Linear rank statistics and the general two-sample problem. Linear rank tests for the location problem, linear rank tests for the scale problem. Tests of the equality of k independent samples. Measures for bivariate samples. Measures of association in multiple comparison. Law of large numbers: weak and strong law.